Finite Group Databasebeta

← #25147269

Subgroups — #25147269

Order 11008.

1012 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583291C211yesmaximal, characteristic, complemented
2C2×#14583118C211yesmaximal, characteristic, complemented
3C2×#14583114C211yesmaximal, characteristic
4C2×#14583111C211yesmaximal, characteristic
5#19137664C211yesmaximal, characteristic, complemented
6#19135917C211yesmaximal, characteristic, complemented
7#19135910C211yesmaximal, characteristic, complemented
8#19135689C211yesmaximal, characteristic, complemented
9#19135672C211yesmaximal, characteristic
10#19135519C211yesmaximal, characteristic, complemented
11#19135319C211yesmaximal, characteristic, complemented
12#19134939C211yesmaximal, characteristic, complemented
13#19134932C211yesmaximal, characteristic, complemented
14#19134420C211yesmaximal, characteristic, complemented
15C43×#2547C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20C22×#10621884C2211yescharacteristic
21C22×#10621882C2211yescharacteristic
22C2×#13063313C2211yescharacteristic
23C2×C4×Dic86C2211yescharacteristic
24C2×C4×D172C2211yescharacteristic
25#14583291—24no—
26#14583118—24no—
27#14583114—24no—
28#14583111—24no—
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063236C2211yescharacteristic
41#14582805C2211yescharacteristic
42#14582801C2211yescharacteristic
43#14582789—21no—
44#14582788—21no—
45#14582770—21no—
46C4×C4⋊Dic43C2211yescharacteristic
47#14582746—21no—
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C2×C4⋊Q8×C43C2211yescharacteristic
53C2×#124×C43C2211yescharacteristic
54C2×#124×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C43×#397—21no—
57C43×#397—21no—
58C43×#391C2211yescharacteristic
59C43×#391C2211yescharacteristic
60C43×#380—21no—
61C43×#380—21no—
62C4×C4⋊C4×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C4×D43—21no—
66C2×#10621885—22no—
67C2×#10621885—22no—
68C2×#10621885—22no—
69C2×#10621885—22no—
70C2×#10621885—41no—
71C2×#10621885—41no—
72C2×#10621883—22no—
73C2×#10621883—22no—
74C2×#10621883—41no—
75C2×#10621884—22no—
76C2×#10621884—22no—
77C2×#10621884—22no—
78C2×#10621884—22no—
79C2×#10621884—41no—
80C2×#10621884—41no—
81C2×#10621882—22no—
82C2×#10621882—22no—
83C2×#10621882—41no—
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88#13063313—22no—
89#13063313D414yes—
90C4×Dic86—22no—
91C4×Dic86—41no—
92C4×D172—22no—
93C4×D172—41no—
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×Dic43⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43—21no—
104C4⋊(C43⋊C8)—22no—
105C4⋊(C43⋊C8)—22no—
106C4⋊(C43⋊C8)—22no—
107#13063249—22no—
108#13063249—22no—
109#13063249—41no—
110#13063249—41no—
111#13063248—22no—
112#13063246—22no—
113#13063246D414yes—
114#13063245—22no—
115#13063236—22no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C22×Q8×C43C2311yescharacteristic
120C22×Q8×C43C2311yescharacteristic
121C22×D4×C43C2311yescharacteristic
122C23×C4×C43—21no—
123C4⋊Q8×C43—22no—
124C4⋊Q8×C43—22no—
125#124×C43—22no—
126#124×C43—22no—
127#124×C43—41no—
128#124×C43—41no—
129C4×D4×C43—22no—
130C4×D4×C43—22no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43D411yescharacteristic
134C2×C4⋊C4×C43D411yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C42×C43C2311yescharacteristic
142C2×C42×C43C2311yescharacteristic
143C2×C42×C43C2311yescharacteristic
144#95×C43—21no—
145#95×C43—21no—
146#95×C43—21no—
147#95×C43—21no—
148#95×C43D411yescharacteristic
149#95×C43D411yescharacteristic
150C24×C43—21no—
151C23×D43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43C2×D412yes—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—42no—
174C22×C4×C43—42no—
175C22×C4×C43—42no—
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2411yescharacteristic
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C2×D172—21no—
187C2×D172—21no—
188C2×D172—21no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172C2×D412yes—
192C2×C4×D43—42no—
193C2×C4×D43—42no—
194C2×C4×D43—81no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86C2×D412yes—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—41no—
204C4⋊C4×C43—41no—
205C4⋊C4×C43—42no—
206C4⋊C4×C43—42no—
207C22⋊C4×C43—42no—
208C22⋊C4×C43—42no—
209C22⋊C4×C43—42no—
210C22⋊C4×C43—42no—
211C22⋊C4×C43—42no—
212C42×C43—21no—
213C42×C43—21no—
214C42×C43—21no—
215C42×C43—21no—
216C42×C43C2×D412yes—
217C42×C43#4112yes—
218#10621885—44no—
219#10621885—44no—
220#10621884—44no—
221#10621884—44no—
222#10621883—44no—
223#10621882—44no—
224(C2×D43)⋊C4—24no—
225(C2×D43)⋊C4—24no—
226(C2×D43)⋊C4—42no—
227(C2×D43)⋊C4—42no—
228(C2×D43)⋊C4—81no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43C2×D412yes—
233Dic43⋊C4—42no—
234C4×Dic43—42no—
235C4×Dic43—81no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8C2×D412yes—
247C2×C43⋊C8#4112yes—
248C23×C43—22no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43C22×D411yescharacteristic
256C22×D43—22no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—41no—
261C22×D43—41no—
262C22×D43—41no—
263Q8×C43—41no—
264Q8×C43—41no—
265Q8×C43—41no—
266Q8×C43—41no—
267Q8×C43—41no—
268Q8×C43—41no—
269Q8×C43—41no—
270Q8×C43—41no—
271D4×C43—22no—
272D4×C43—22no—
273D4×C43—41no—
274D4×C43—41no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—84no—
301C2×C4×C43#12112yes—
302C2×C4×C43#12112yes—
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C22×D411yescharacteristic
305C2×C4×C43C2×#4111yescharacteristic
306C2×C4×C43C2×#4111yescharacteristic
307C2×C4×C43H(5,𝔽2)11yescharacteristic
308C2×C4×C43H(5,𝔽2)11yescharacteristic
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318D172—22no—
319D172—22no—
320D172—41no—
321D172—41no—
322C4×D43—84no—
323Dic86—22no—
324Dic86—22no—
325Dic86—41no—
326Dic86—41no—
327C43⋊C8—22no—
328C43⋊C8—22no—
329C43⋊C8—41no—
330C43⋊C8—41no—
331#25381—431nomaximal, Sylow
332C22×C43—42no—
333C22×C43—42no—
334C22×C43—42no—
335C22×C43—81no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43—81no—
339C22×C43C2×#12111yescharacteristic
340C22×C43D4211yescharacteristic
341C22×C43#55011yescharacteristic
342C22×C43#57511yescharacteristic
343C22×C43#57511yescharacteristic
344C22×C43#57711yescharacteristic
345C22×C43#57811yescharacteristic
346C2×D43—42no—
347C2×D43—42no—
348C2×D43—42no—
349C2×D43—81no—
350C2×D43—81no—
351C2×D43—81no—
352C2×D43—81no—
353C4×C43—22no—
354C4×C43—22no—
355C4×C43—41no—
356C4×C43—41no—
357C4×C43—41no—
358C4×C43—41no—
359C4×C43—81no—
360C4×C43—81no—
361C4×C43—81no—
362C4×C43#53211yescharacteristic
363C4×C43#54011yescharacteristic
364C4×C43D4211yescharacteristic
365C4×C43#54611yescharacteristic
366Dic43—42no—
367Dic43—42no—
368Dic43—81no—
369C2×#497—431no—
370C2×#464—431no—
371C2×#463—431no—
372C2×#463—431no—
373#2547D4311yescharacteristic, complemented
374#2367—431no—
375#2056—431no—
376#2055—431no—
377#2015—431no—
378#2012—431no—
379#1981—431no—
380#1940—431no—
381#1878—431no—
382#1877—431no—
383#1762—431no—
384C2×C43—82no—
385C2×C43#242811yescharacteristic
386C2×C43#304011yescharacteristic
387C2×C43#304611yescharacteristic
388C2×C43#326711yescharacteristic
389C2×C43#326911yescharacteristic
390C2×C43#340111yescharacteristic
391C2×C43#340211yescharacteristic
392D43—82no—
393C22×Q16—431no—
394C22×Q16—431no—
395C22×SD16—431no—
396C22×SD16—431no—
397C22×SD16—431no—
398C22×D8—431no—
399C2×C4⋊Q8C2×D4311yescharacteristic
400C2×#124—431no—
401C2×#124C2×D4311yescharacteristic
402C2×#124C2×D4311yescharacteristic
403C2×C4×Q8—431no—
404C2×C4×D4—431no—
405C2×C4×D4C2×D4311yescharacteristic
406#497—864no—
407#464—864no—
408#463—864no—
409#463—864no—
410C2×C4⋊C8—431no—
411C2×C4⋊C8—431no—
412C2×C4⋊C8—431no—
413C2×#103—431no—
414C2×#103—431no—
415C2×#103—431no—
416C2×#103—431no—
417C2×#103—431no—
418C2×#102—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×#97—431no—
422#397—21no—
423#397—21no—
424#391—431no—
425#391C2×D4311yescharacteristic
426#391C2×D4311yescharacteristic
427#390—431no—
428#388—861no—
429#388—861no—
430#385—861no—
431#380—21no—
432#380—21no—
433C4×C4⋊C4—431no—
434C4×C4⋊C4C2×D4311yescharacteristic
435C4×C22⋊C4—861no—
436#340—431no—
437#340—431no—
438#336—431no—
439#336—431no—
440C43#2538111yescharacteristic, complemented, Sylow
441C22×Q8—431no—
442C22×Q8C22×D4311yescharacteristic
443C22×Q8C22×D4311yescharacteristic
444C22×D4—431no—
445C22×D4C22×D4311yescharacteristic
446C23×C4—21no—
447C23×C4—861no—
448C2×Q16—862no—
449C2×Q16—862no—
450C2×Q16—862no—
451C2×Q16—862no—
452C2×Q16—1721no—
453C2×Q16—1721no—
454C2×SD16—862no—
455C2×SD16—862no—
456C2×SD16—862no—
457C2×SD16—862no—
458C2×SD16—862no—
459C2×SD16—862no—
460C2×SD16—1721no—
461C2×SD16—1721no—
462C2×SD16—1721no—
463C2×D8—862no—
464C2×D8—862no—
465C2×D8—1721no—
466C22×C8—431no—
467C22×C8—431no—
468C22×C8—431no—
469C22×C8—431no—
470C4⋊Q8—22no—
471C4⋊Q8—22no—
472#124—22no—
473#124—22no—
474#124—41no—
475#124—41no—
476#124—434no—
477#124—862no—
478C4×Q8—862no—
479C4×Q8—1721no—
480C4×D4—22no—
481C4×D4—22no—
482C4×D4—862no—
483C4×D4—1721no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—431no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4C22⋊D4311yescharacteristic
490C2×C4⋊C4C22⋊D4311yescharacteristic
491C2×C4⋊C4C22×D4311yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4—861no—
502C2×C42—861no—
503C2×C42—861no—
504C2×C42C22×D4311yescharacteristic
505C2×C42C22×D4311yescharacteristic
506C2×C42C22×D4311yescharacteristic
507C4⋊C8—862no—
508C4⋊C8—862no—
509C4⋊C8—862no—
510#103—862no—
511#103—862no—
512#103—862no—
513#103—1721no—
514#103—1721no—
515#102—434no—
516#102—862no—
517#102—862no—
518#97—862no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—861no—
524#95—861no—
525#95—861no—
526#95C22⋊D4311yescharacteristic
527#95C22⋊D4311yescharacteristic
528C24—21no—
529C24—861no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—432no—
543C2×Q8—861no—
544C2×Q8—861no—
545C2×Q8—861no—
546C2×Q8—861no—
547C2×Q8—861no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—432no—
554C2×D4—861no—
555C2×D4—861no—
556C2×D4—861no—
557C2×D4—861no—
558C2×D4—861no—
559C2×D4D4×D4312yes—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—3441no—
570C22×C4—1722no—
571C22×C4—1722no—
572C22×C4C2×C22⋊D4311yescharacteristic
573C22×C4C2×C22⋊D4311yescharacteristic
574C22×C4C2×C22⋊D4311yescharacteristic
575C22×C4C2×C22⋊D4311yescharacteristic
576C22×C4C2×C22⋊D4311yescharacteristic
577C22×C4C2×C22⋊D4311yescharacteristic
578C22×C4C23×D4311yescharacteristic
579Q16—1724no—
580Q16—1724no—
581SD16—1724no—
582SD16—1724no—
583SD16—1724no—
584D8—1724no—
585C2×C8—432no—
586C2×C8—432no—
587C2×C8—861no—
588C2×C8—861no—
589C2×C8—861no—
590C2×C8—861no—
591C2×C8—861no—
592C2×C8—861no—
593C2×C8—861no—
594C2×C8—861no—
595C2×C8—861no—
596C2×C8—861no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—41no—
600C4⋊C4—41no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—432no—
604C4⋊C4—861no—
605C4⋊C4—861no—
606C4⋊C4—861no—
607C4⋊C4—1722no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—864no—
614C22⋊C4—864no—
615C22⋊C4—3441no—
616C22⋊C4—1722no—
617C22⋊C4—1722no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—3441no—
623C42—1722no—
624C42D4×D4312yes—
625C42#1062190012yes—
626C23—22no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—862no—
634C23—1721no—
635C23—1721no—
636C23—1721no—
637C23—1721no—
638C23—1721no—
639C23—1721no—
640C23C22×C22⋊D4311yescharacteristic
641Q8—41no—
642Q8—41no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—862no—
650Q8—862no—
651Q8—1721no—
652Q8—1721no—
653D4—22no—
654D4—22no—
655D4—41no—
656D4—41no—
657D4—862no—
658D4—862no—
659D4—1721no—
660D4—1721no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—84no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—3444no—
690C2×C4—1721no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4—1721no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4#1306329612yes—
698C2×C4#1306329612yes—
699C2×C4C2×D4×D4311yescharacteristic
700C2×C4C2×D4×D4311yescharacteristic
701C2×C4#41×D4311yescharacteristic
702C2×C4C2×#1062190011yescharacteristic
703C2×C4#1306337011yescharacteristic
704C2×C4#1306337111yescharacteristic
705C8—862no—
706C8—862no—
707C8—1721no—
708C8—1721no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—3441no—
717C22—3441no—
718C22—3441no—
719C22—3441no—
720C22—1722no—
721C22—1722no—
722C22—1722no—
723C22C2×#1306329611yescharacteristic
724C22D4×C22⋊D4311yescharacteristic
725C22#1458356811yescharacteristic
726C22#1458369711yescharacteristic
727C22#1458369711yescharacteristic
728C22#1458370711yescharacteristic
729C22#1458371411yescharacteristic
730C4—22no—
731C4—22no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—81no—
737C4—81no—
738C4—81no—
739C4—3441no—
740C4—1722no—
741C4—1722no—
742C4#1458344411yescharacteristic
743C4#1458350211yescharacteristic
744C4#1458353311yescharacteristic
745C4#1458354611yescharacteristic
746C2—82no—
747C2—3442no—
748C2#1913817911yescharacteristic
749C2#1914408511yescharacteristic
750C2#1914414111yescharacteristic
751C2#1914612111yescharacteristic
752C2#1914614611yescharacteristic
753C2#1914766111yescharacteristic
754C2#1914767011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2547C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
hypercenter#2547D43
hypocenterC43#25381
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2547

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#14583291C2semidirect
2. C2×#14583118C2semidirect
5. #19137664C2semidirect
6. #19135917C2semidirect
7. #19135910C2semidirect
8. #19135689C2semidirect
10. #19135519C2semidirect
11. #19135319C2semidirect
12. #19134939C2semidirect
13. #19134932C2semidirect
14. #19134420C2semidirect
15. C43×#2547C2semidirect
373. #2547D43semidirect
440. C43#25381semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145832912
C2×#145831182
C2×#145831142
C2×#145831112
#191376642
#191359172
#191359102
#191356892
#191356722
#191355192
#191353192
#191349392
#191349322
#191344202
C43×#25472
#2538143